Swaying oscillons in the signum-Gordon model

TL;DR

This paper introduces a new class of finite-energy, strictly periodic oscillons in the (1+1)-dimensional signum-Gordon model that move periodically in space and are explicitly constructed using polynomial solutions.

Contribution

The paper presents explicit polynomial solutions for oscillons in the signum-Gordon model, demonstrating their finite energy, size, and periodic motion, which is a novel class of solutions.

Findings

Oscillons are strictly periodic and finite in energy and size.

Explicit polynomial solutions for oscillons are constructed.

Oscillons exhibit periodic motion in space within the model.

Abstract

We present a new class of oscillons in the (1+1)-dimensional signum-Gordon model. The oscillons periodically move to and fro in the space. They have finite total energy, finite size, and are strictly periodic in time. The corresponding solutions of the scalar field equation are explicitly constructed from the second order polynomials in the time and position coordinates.